What is (\partial)/(\partial y)(1/x+1/y) ?

The answer to (\partial)/(\partial y)(1/x+1/y) is -1/(y^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(1/x+1/y)

\frac{\partial}{\partial y} (\frac{1}{x} + \frac{1}{y})

- \frac{1}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{1}{x} + \frac{1}{y})

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (\frac{1}{x}) + \frac{\partial}{\partial y} (\frac{1}{y})

\frac{\partial}{\partial y} (\frac{1}{x}) = 0

\frac{\partial}{\partial y} (\frac{1}{y}) = - \frac{1}{y ^{2}}

= 0 - \frac{1}{y ^{2}}

Simplify

= - \frac{1}{y ^{2}}

\int 5 e^{5 x} sin (e^{5 x}) d x

\int 2 cos (x) d x

x \to 5 lim (cos (\frac{1}{x - 5}))

y = x^{2} - 2 x + 3, x = - 2, x = 1

x \to 0 + lim (1 + x^{5 t a n (x)})

What is (\partial)/(\partial y)(1/x+1/y) ?
The answer to (\partial)/(\partial y)(1/x+1/y) is -1/(y^2)